Using Learning Curves

In the introduction to my previous E-Learning Curve Blog post, focussing on the topic of learning curves, I referenced the axiom that ‘practice makes perfect’ – the concept that the acquisition and improvement of new skills, knowledge or expertise are broadly predicated upon the learner’s facility and willingness to rehearse and become more proficient in the tasks or activities being practised.

This is not news. We have all experienced this process, and Behaviorists would venture to assert that perhaps we know it intuitively. What may be more surprising is that the rate and shape of improvement of learning can be described geometrically on a curve.

The concept of the learning curve illustrates a simplified model of learning in which knowledge of a given subject is acquired through a progression of steps. Figure 1 shows a model of an idealized (and simplified, and in no way scientifically nor pedagogically accurate) learning curve applied to Bloom’s Taxonomy. At the lowest levels of the curve, the learner is a novice who then progresses through the various stages of cognitive development, where at each stage they increase in competency until (perhaps up to a decade and / or 10,000 practice hours later) they become an expert, with an overarching competency in the domian being studied.

Figure 1. Bloom’s Taxonomy charted on a learning curve

The learning curve has substantial implications for e-learning: it suggests that practice always helps improve performance, but that the most dramatic improvements happen first, with smaller and smaller incremental improvements being accrued over time. Another implication is that with sufficient practice, learners can achieve comparable levels of performance. For example, extensive practice on mental arithmetic (Staszewski, reported in Delaney et al., 1998) and on digit memorization have turned average individuals into high performers in the discipline.

The learning curve was devised from the historical observation that individuals who perform repetitive tasks demonstrate an improvement in performance as the task is repeated over time. It was first studied empirically in the 1930’s by T. P. Wright. In his text Factors Affecting the Cost of Airplanes, Wright drew three conclusions upon which the current theory and practice surrounding learning curves are based:

The time required to perform a task decreases as the task is repeated

The amount of improvement decreases as more units are produced

The rate of improvement has sufficient consistency to allow its use as a prediction tool

In this study, Wright concluded

that consistency in improvement has been found to exist in the form of a constant percentage reduction in time required over successively doubled quantities of units produced. The constant percentage by which the costs of doubled quantities decrease is called the Rate of Learning.